(CNN)Everyone seems to have an opinion on the ever-evolving story of Charlie Gard, the British infant suffering from a fatal genetic disease. President Donald Trump and the Pope have weighed in, and now Vice President Pence has done so as well.

Pence told conservative talk show host Rush Limbaugh, "The heartbreaking story of the 11-month-old Charlie Gard in England is a story of single-payer health care ... the American people ought to reflect on the fact that for all the talk on the left about single payer, that's where it takes us."

Pence's comments are alarming. He has politicized a tragic story -- and in doing so tried to undermine single-payer health care systems, which exist in Canada and Great Britain and which many think should be established in the US.

Under a single-payer system, the government would cover a certain basic amount of health care for everyone. Profit-making private insurers would no longer extract money out of the system as they now do to maximize shareholder profits. Rather, money allocated for health could be used more directly to help patients.

Medicare, Medicaid and the US Department of Veterans Affairs health system are all examples of single payers for patients covered under these programs. The Affordable Care Act is a complex, hybrid model, but is a small step in the direction of single payer, increasing government funds and involvement to ensure that millions of Americans who would otherwise lack health insurance now receive it.

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For Pence and other right wingers, "single-payer health care" is code for Obamacare.

Even though the Republican Senate now lacks the votes to repeal and replace the ACA, President Trump is tweeting to repeal the act now and replace it in the future.

Obamacare, of course, is not perfect. Even Democrats say that it needs to be improved -- though not scrapped. It has provided care to millions of Americans. Still, Congress needs to act to lower premiums and improve the health care system as a whole in other ways.

And this is where Pence's comment about Charlie Gard is deeply flawed, not only because it unfairly attacks single-payer systems, but also because it conflates single-payer systems with judicial rulings concerning patients' rights. Gard's legal battles -- and his family's losses thus far -- reflect the goals of the British and European court systems to prevent an infant from needless suffering, and not the costs or systems of care.

Notably, the European Court of Human Rights upheld the British court's judgment and ruled against the continuation of life support because they think the infant is now suffering without hope, or will do so with experimental treatment.

And while I personally think Charlie's parents should be allowed to decide whether his life support continues, Pence is suggesting the British judges are making their decisions because they are rationing health care. That is simply not the case.

Pence's argument also falls particularly short because the single-payer systems we now have -- Medicare, Medicaid and the VA -- don't necessarily deprive patients of choice or rights, and allow patients to make their own decisions concerning what end-of-life care to receive. Patients can thus be in single-payer plans but still choose, through their families and/or advanced directives, to receive so-called heroic measures, even when they have no chance of recovering.

Courts generally operate separately. Judges can intervene either to stop or start care, depending on the details of the case.

In fact, Americans have often been blocked from making their own health care decisions by conservative rulings.

Take Terri Schiavo, who in 1990 had a heart attack and suffered severe brain damage. Her husband vigorously pursued treatment, but unsuccessfully. After several years on life support, with no chance of recovery, her husband, who was her legal guardian, sought to remove her feeding tube. She did not have a living will, but he and other witnesses presented evidence that Terri had said that she would not want to be maintained on life support if she had no hope of recovering.

When her parents objected, the Florida courts sided with her husband and denied the parents' later appeals.

Gov. Jeb Bush then signed "Terri's Law," ordering that the tube be reinserted. Yet the Florida Supreme Court then ruled that the law was unconstitutional. In response, President George W. Bush signed a bill, transferring jurisdiction of her case to federal, rather than state courts. But federal judges denied her parents' appeals. Here, conservatives -- including President Trump's Republican predecessor -- sought to block what a patient and her legal guardian wanted. Schiavo died in 2005 after her feeding tube was removed.

And while decisions about Charlie's fate remain unclear -- the UK High Court is now deciding whether he can try an experimental drug from the US -- we can choose how to respond to Charlie's and similar situations, both as individuals and as a society.

To help him and other infants with untreatable genetic diseases, we need to continue -- not eliminate -- insurance coverage for families and children who may now or one day confront devastating diseases, and we should support more research to learn how better to address these conditions.